# The Associative Property of Addition

🏆Practice associative property

We can use this property in three ways:

1. We start by adding the first and the third addend, solve the sum and then add the second addend to the result.

We will place in parentheses around the addends that we want to group first to give them priority in the order of operations.

The associative property of addition also works in algebraic expressions, but not in subtraction operations.
Let's define the associative property of addition as:
$a+b+c=(a+b)+c=a+(b+c)=(a+c)+b$

## Test yourself on associative property!

$$94+12+6=$$

Let's look at an example:
$2+10X+2X=2+12X$

We will obtain an expression equivalent to the first expression since the associative property does not change the result.

Let's put a number in place of X to verify :

$X=3$
$2+10\times 3+2\times 3=2+12\times 3$

$2+30+6=2+36$
$38=38$

As we can see, after applying the associative property and adding the last two terms of the expression(the second and the third), and then adding the first term to the sum, the result is the same.
The associative property is an important and useful tool, so we recommend that you practice as much as possible until you can use it without thinking!

## Example exercises

### Exercise 1

$7+8+12=$

Solution:

$7+8+12=15+12=27$

$27$

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### Exercise 2

$94+12+6=$

Solution:

$94+6+12=100+12=112$

$112$

### Exercise 3

$13+37+45=$

$50+45=95$

$95$

Do you know what the answer is?

### Exercise 4

$4:2×\left(5+4+6\right)=$

Solution:

$2×\left(5+4+6\right)=$

$2\times(5+4+6)=$

$2\times(15)=$

$2\times(15)=30$

$30$

### Exercise 5

$7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=\text{?}$

Solution:

$7\frac{2}{3}+6\frac{1}{6}+4\frac{1}{9}=$

$=7\frac{12}{18}+6\frac{3}{18}+4\frac{2}{18}=17+\frac{12+3+2}{18}$

$=7\frac{17}{18}=17\frac{17}{18}$

$17\frac{17}{18}$

### Exercise 6

$6\times\frac{4}{5}x+7\times\frac{1}{2}x+4\times\frac{1}{3}x\times7.3x=\text{?}$

Solution:

$6\frac{4}{5}X+7\frac{1}{2}X+4\frac{1}{3}X\times7\frac{3}{10}X=\frac{34}{5}X+\frac{15}{2}X+\frac{13}{3}X\times\frac{73}{10}X$

$=\frac{68}{10}X+\frac{75}{10}X+\frac{13\times73}{3\times10}X²$

$=\frac{68+75}{10}X+\frac{949}{30}X²$

$=\frac{143}{10}X+31\frac{19}{30}X²=14.3X+31\frac{19}{30}X²$

$14.3x+31\frac{19}{30}x²$

### Exercise 7

$4.1\times1.6\times3.2+4.7=\text{?}$

Solution:

$4.1\times1.6\times3.2+4.7=\text{?}$

$=4\frac{1}{10}\times1\frac{6}{10}\times3\frac{2}{10}+4\frac{7}{10}=$

$\frac{41}{10}\times\frac{16}{10}\times\frac{32}{10}+\frac{47}{10}=\frac{656}{100}\times\frac{32}{10}+\frac{47}{10}$

$\frac{41\times16}{10\times10}=\frac{656}{100}=\frac{656\times32}{100\times10}+\frac{47}{10}=$

$=\frac{20992}{1000}+\frac{4700}{1000}$

$=\frac{25692}{1000}=25.692$

$25.692$

Do you think you will be able to solve it?

## examples with solutions for the associative property of addition

### Exercise #1

$6:2+9-4=$

### Step-by-Step Solution

According to the order of operations, we first solve the division exercise, and then the subtraction:

$(6:2)+9-4=$

$6:2=3$

Now we place the subtraction exercise in parentheses:

$3+(9-4)=$

$3+5=8$

$8$

### Exercise #2

$3\times5\times4=$

### Step-by-Step Solution

According to the order of operations, we must solve the exercise from left to right.

But, this can leave us with awkward or complicated numbers to calculate.

Since the entire exercise is a multiplication, you can use the associative property to reorganize the exercise:

3*5*4=

We will start by calculating the second exercise, so we will mark it with parentheses:

3*(5*4)=

3*(20)=

Now, we can easily solve the rest of the exercise:

3*20=60

60

### Exercise #3

$3+2-11=$

### Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right:

$3+2=5$

$5-11=-6$

$-6$

### Exercise #4

$4+5+1-3=$

### Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right:

$4+5=9$

$9+1=10$

$10-3=7$

7

### Exercise #5

$24:8:3=$

### Step-by-Step Solution

According to the order of operations, we solve the exercise from left to right since the only operation in the exercise is division:

$24:8=3$

$3:3=1$

$1$